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33 Copyright © Wright Group/McGraw-Hill STUDY LINK 21 Estimation 247 Name Date Time Class Medians for: Step Length _______________ Steps in 1 Minute ______________ A group of fifth-grade students in New Zealand are going camping. They will hike from Wellington to Ruapehu. Then they will follow a trail for another 1 2mile to their campsite. Use the map on this page (Scale: 1 inch 400 miles) as well as your class median step length, and number of steps in 1 minute, to make the following estimates. (Reminder:1 mile 5,280feet) 1. About how many miles is it from Wellington to Ruapehu? __________________ 2. About how many miles is it from Wellington to the campsite? _______________ 3. About how long would it take the students to arrive at their campsite, if they don't make any stops? ________________________ 4. Each day, the students will hike for 12 hours and take 12 hours for stops to eat, rest, and sleep. If they leave at 7:00 A.M. on a Monday morning, at about what time, and on what day would you expect them to arrive at their campsite? Time: About _________ Day: __________________ Try This 5. Suppose the students take a bus from Wellington to Mt. Cook and then hike to a campsite at the top of the mountain. Would they have to hike more or less than the distance they hiked to their campsite at Ruapehu? 6. 4815  7. 24,029 26,840 39,492  8. 36 3  9. 35 17  NEW ZE A LAND Wellington Auckland DunedinChristchurch Mt. Cook RuapehuNorth Island South Island 0 200 400 1 inch represents 400 miles Elevations: 12,349 ft Mt. Cook 9,175 ft Ruapehu N WE S (unit) (unit) (unit) Practice

34 Copyright © Wright Group/McGraw-Hill LESSON 21 Name Date Time Estimation Strategies 1. Rosie wants to estimate the number of flowers in this picture. Her estimation strategy has 3 steps. Find the 3 steps in the list of strategies below. Write 1 next to the step that you think should be done 1st. Write 2 next to the step that you think should be done 2nd. Write 3 next to the step that you think should be done 3rd. _________ Count every flower. Count the number of flowers in one section. _________ Make a guess. Multiply this number by 4. _________ Ask someone how many flowers are in the picture. Draw lines to divide the picture into four equal sections. 2. Could you use Rosie’s strategy to estimate only the number of all-black flowers in the picture? 3. Explain why or why not.

35 Copyright © Wright Group/McGraw-Hill Name Date Time Work with a partner. Use a sample page from the residential section of a telephone book to estimate the total number of names listed on 10 pages of the telephone book. Develop an estimation strategy by answering the following questions. 1. How might dividing the page into equal portions be useful? 2. What information could you get from the sample page that would let you know how many names are on 10 pages without counting them all? Record your estimate. 3. About ________ names are on 4. About ________ names are on 1 page of the telephone book. 10 pages of the telephone book. Work with a partner. Use your sample page from the residential section of a telephone book to estimate the total number of names listed on 10 pages of the telephone book. Develop an estimation strategy by answering the following questions. 1. How might dividing the sample page into four equal sections be useful? 2. What information could you get from the sample page that would let you know how many names are on 10 pages without counting them all? Record your estimate. 3. About ________ names are on 4. About ________ names are on 1 page of the telephone book. 10 pages of the telephone book. LESSON 00 Estimating Totals LESSON 21 Estimating

STUDY LINK 22 Number Hunt Copyright © Wright Group/McGraw-Hill 36 Name Date Time Reminder:A means Do not use a calculator. Use the numbers in the following table to answer the questions below. You may not use a number more than once. 1. Circle two numbers whose sum is 832. 2. Make an X in the boxes containing three numbers whose sum is 57. 3. Make a check mark in the boxes containing two prime numbers whose sum is 42. 4. Make a star in the boxes containing two numbers whose sum is 658. 5. Make a triangle in the boxes containing two numbers whose sum is 105.7. Explain how you found the answer. Solve Problems 6–9 using any method you want. Show your work in the space below. 6. 3,804 768  7. 2.83 1.57  8. 33 148 65  9. 1.055 0.863  10. 73 26  11. 727 519  12. 27 9  13. 4 3 4 ∑ 19 85.2 533 571 88.2 525 20 17.5 400 261 20.5 125 7 23 901 30 Practice 13–17

LESSON 22 Name Date Time Modeling with Base-10 Blocks 37 Copyright © Wright Group/McGraw-Hill Example: Work with a partner. Choose a problem below. Use the base-10 blocks to model the problem. Have your partner solve the problem and record the answer using the partial-sums method. Compare your model with your partner's solution. Reverse roles and continue until all problems are solved. 1. 456  53 Add 100s Add 10s Add 1s 3. 271  653 Add 100s Add 10s Add 1s 100s + 10s 1s 500 70 6 ++ 100s 10s 1s 231 345 Add 100s 5 0 0 Add 10s 7 0 Add 1s 6 576 2. 764  208 Add 100s Add 10s Add 1s 4. 521  455 Add 100s Add 10s Add 1s

LESSON 22 Name Date Time Place-Value Strategies 38 Copyright © Wright Group/McGraw-Hill Use your favorite addition algorithm to solve the first problem in each column. Then use the answer to the first problem in each column to help you solve the remaining problems. d. 7,401 2,699 d. 3,058  2,181 c. 7,401 2,689 c. 3,058  2,582 b. 7,401 2,669 b. 3,058  2,082 a. 7,401 2,679 a. 3,058  2,282 2. 7,401 2,659 1. 3,058  2,182 3. Explain the strategy you used to solve the problem sets above.

STUDY LINK 23 Another Number Hunt 39 Name Date Time Copyright © Wright Group/McGraw-Hill Use the numbers in the following table to answer the questions below. You may not use a number more than once. 1. Circle two numbers whose difference is 152. 2. Make an X in the boxes of two numbers whose difference is 25.6. 3. Make a check mark in the boxes of two numbers whose difference is greater than 1,000. 4. Make a star in the boxes of two numbers whose difference is less than 10. 5. Make a triangle in the boxes of two numbers whose difference is equal to the sum of 538 and 259. 6. Use diagonal lines to shade the boxes of two numbers whose difference is equal to 4 2. Subtract. Show your work for one problem on the grid below. 7. 247 186  8. 405 268 9. 24.5 18.7  10. 62.7 43.85 11. 488  12. 81,447 2,571  13. $451.17 $2.81  14. 14 º 7  15. 98 7  17 15 9 75.03 100.9 803 25 451 1,500 5,000 1 3,096 299 75.340.03 703 Practice 13–17

LESSON 23 Name Date Time Make and Break Apart 40 Copyright © Wright Group/McGraw-Hill Directions Make 10s by putting your wooden craft sticks or straws into bundles of 10. Use these bundles to model the subtraction problems. Then use your models to solve the problems. Example: 22 – 7 To begin, you need 2 bundles of 10 and 2 ones. To subtract 7, you need to break apart one bundle. Now you have 12 ones. Remove 7 ones. Solution: 1. 10 4  2. 32 6  3. 71 23  4. 22 9  5. 56 38  6. 110 62  15 1010222 10515 7

LESSON 24 Name Date Time Situation Diagrams 41 Copyright © Wright Group/McGraw-Hill Start EndChange Quantity Quantity Difference per in all

LESSON 24 Name Date Time Using Open Number Sentences 42 Problem 1:At breakfast, the temperature outside was 47 F. By lunchtime, the temperature was 63 F. How many degrees warmer was it by lunchtime? Open number sentence: Solution: Answer: (unit) Name Date Time Problem 2:Mary had $32.50 in her savings account. After she withdrew some money, she had $17.25 left. How much money did she withdraw? Open number sentence: Solution: Answer: (unit) Name Date Time Problem 3:The school library has 486 fiction books and 321 nonfiction books. How many books does the library have in all? Open number sentence: Solution: Answer: (unit) Problem 4:Mrs. Snow is 49 years old. Her son, Kevin, is celebrating his 24th birthday today. Mr. Snow is 6 years older than Mrs. Snow. How old was Mrs. Snow when Kevin was born? Open number sentence: Solution: Answer: (unit) Name Date Time Copyright © Wright Group/McGraw-Hill

STUDY LINK 2 4 Open Sentences and Number Stories 43 Name Date Time Copyright © Wright Group/McGraw-Hill Read each problem. Fill in the blanks and solve the problem. 1. Althea and her brother collect baseball cards. Althea has 148 cards. Her brother has 127 cards. How many cards do they have altogether? a. List the numbers needed to solve the problem. b. Describe what you want to find. c. Open number sentence: d. Solution: e. Answer: (unit) 2. Mark bought a hamburger for $3.89 and a drink for $1.49. If he paid with a $20 bill, how much change did he receive? a. List the numbers needed to solve the problem. b. Describe what you want to find. c. Open number sentence: d. Solution: e. Answer: (unit) 3. Fran has four pieces of ribbon. Each piece of ribbon is a different length: 0.6 meters long, 1.15 meters long, 1.35 meters long, and 0.925 meters long. How many meters of ribbon does Fran have in all? a. List the numbers needed to solve the problem. b. Describe what you want to find. c. Open number sentence: d. Solution: e. Answer: (unit) 223

Start EndChange LESSON 24 Name Date Time Using Situation Diagrams 44 Copyright © Wright Group/McGraw-Hill ◆ Use the information in each problem to fill in the diagram. ◆ Use a ? to show the missing number. ◆ Write an open number sentence with the information from the diagram. 1. Two angles of a triangle measure 45 and 55 . What is the sum of the measures of the two angles? Open number sentence: 2. There are 64 orange and green tennis balls in a basket. If 35 of them are orange, how many tennis balls are green? Open number sentence: 3. Elvin had $15.00 to spend at the school bazaar. He spent $12.75. How much money did he have left? Open number sentence: Start EndChange Start EndChange 4. a. At 7 A.M., the temperature is 76 F. The temperature is expected to drop 17 by 4 P.M. What will the temperature be at 4 P.M.? Open number sentence: b. What would the temperature be at 4 P.M. if the temperature increased by 17 ? Open number sentence:

LESSON 24 Name Date Time Writing Open Number Sentences 45 Copyright © Wright Group/McGraw-Hill Write an open number sentence and solve the problem. 1. Chan brought his collection of 1,500 sports cards to school. He has 156 basketball cards and 625 football cards. The rest were baseball cards. How many baseball cards did Chan bring? a. Open number sentence: b. Solution: c. Answer: (unit) 2. Abdul took a bus downtown to see a movie. The bus ride to the theater took 15 minutes. If the movie was 2 1 4hours long, how many hours and minutes was Abdul away from home? a. Open number sentence: b. Solution: c. Answer: (unit) 3. Julie paid $14.08 to fill her gas tank with 10 gallons of gas before starting a trip from Chicago to Topeka, Kansas. After driving about 305 miles, she bought 10 more gallons of gas in Iowa and paid $11.85. How much more did she pay for a gallon of gas in Chicago than in Iowa? a. Open number sentence: b. Solution: c. Answer: (unit)

STUDY LINK 2 5 Comparing Reaction Times Copyright © Wright Group/McGraw-Hill 46 114 Name Date Time 6. 2,683 2,939  7. 3,702 º 8  8. 604 86  9. 39 3  Use your Grab-It Gauge. Collect reaction-time data from two people at home. At least one of these people should be an adult. 1. 2. 3. Median times: 4. Median times: Left hand Left hand Right hand Right hand 5. How do the results for the two people compare to your class data? Person 1 Left Right Person 2 Left Right Practice

LESSON 25 Name Date Time Decimal Number-Line Puzzles 47 Copyright © Wright Group/McGraw-Hill Step 1:Clear your calculator. Look at the number line. Step 2:Enter the end number, subtract the start number, and divide by the number of jumps between. The result is the interval number. Step 3:Enter the start number and add the interval number. This is the first missing number. Add the interval again to get the next missing number, and so on. Example: End number start number difference 6 4 2 Difference hops interval 2 5 0.4 4 0.4 4.4; 4.4 0.4 4.8; 4.8 0.4 5.2; 5.2 0.4 5.6; 5.6 0.4 6.0 1. Jumps: 2. Jumps: 3. Jumps: 1.349.38 1.44.2 66.8 4.0 4.4 4.8 5.2 5.6 6.0 4. Jumps: 4.56831.976 Try This

LESSON 25 Name Date Time Interpreting Data 48 Copyright © Wright Group/McGraw-Hill 1. Organize the median reaction times for right and left hands for your class by gender—one set of data for girls and one set of data for boys. Data Landmarks Girls Boys Minimum Maximum Range Mode Median Mean 2. a. Who has the faster reaction times, boys or girls? b. Which landmark did you use to decide? c. Why? 3. a. Suppose you put names in a hat and, without looking, pulled the name of one boy and one girl. How would you use the data from your class to predict who would be faster? b. Which landmark would you use to decide? c. Why? 4. a. What true statements can you make about the data? b. How might these statements, called findings, be used by your class? c. Could your findings have importance to activities outside of school? d. What kind of picture or graph would help people understand your findings? Use the questions below to interpret the data. Write your answers on a separate sheet of paper.

49 Name Date Time Copyright © Wright Group/McGraw-Hill 0.01 1 9—10 4 — 5 7—10 2—3 5 — 8 5 — 6 7 —8 3—10 1—5 1—10 0 1—6 1— 8 1 — 3 3—8 1—2 0 1—— 100 19—20 8 —10 , 2—54 —10, 1—42 —8, 50——10 0 3—46 — 8 , 3—56 — 10 , 2—4,, 3—6,4—8,5—10,10—20, - 0.5 0 45% 0.45 40%0.40 35%0.35 30%0.30 0.25 20 %0.20 15%0.1 5 10 %0.10 5 %0.05 0.00 50% 25% 0% 0.375 0 .33 0.16 0.125 95 %0.95 90%0.90 85%0.85 80%0.80 0.75 70%0.70 65 %0.65 60 %0.60 55%0.55 1.00 10 0% 0.875 0.83 0.66 0.625 75% - - - 99——100 0.99 50–50 CERTAIN IMP OSS IBLE 1—2 V E R Y I K E L Y U N L V E R Y L I K E L Y L KI L Y E E X T R E M E L Y U N L I K E L Y E X T R E M E L YU N L I K E L Y 50–50 CHANCE L I K E L Y STUDY LINK 2 6 How Likely Is Rain? 128 Phrase Percent Unlikely 30% Very likely Very unlikely Likely Extremely unlikely Percent Phrase 30% Unlikely 5% 99% 20% 80% 35% 65% 45% Many years ago, weather reports described the chances of rain with phrases such as very likely, unlikely,and extremely unlikely. Today, the chances of rain are almost always reported as percents. For example, “There is a 50% chance of rain tonight.” 1. Use the Probability Meter Poster to translate phrases into percents. 2. Use the Probability Meter Poster to translate percents into phrases.

LESSON 26 Name Date Time 50 Copyright © Wright Group/McGraw-Hill Cut out the cards and order them from smallest to largest. Use the table in the front of the journal to help you. Order Fractions, Decimals, Percents 1 2 33 1 3%0.25 3 4 20% 0.60 4 5 0.10 30% 0.70 19 0 12 1 2% 0.625 87 1 2% 2 3 16 2 3%

LESSON 26 Name Date Time Making Spinners 51 Copyright © Wright Group/McGraw-Hill Choosing a Pants Color There is a 30% chance of choosing blue pants. There is a 1 4chance of choosing black pants. There is a 0.1 chance of choosing white pants. There is twice the probability of choosing red pants as there is of choosing white pants. There is a 15 out of 100 chance of choosing brown pants. Choosing a Favorite Color 28% of the people said red was their favorite color. 1 3of the people reported that blue was their favorite color. One-half as many people favored white as favored blue. 0.1 of the people chose brown as their favorite color. 3 out of 25 people named black as their favorite color. Drawing Colored Chips from a Bag There is a 1 out of 5 chance of drawing a white chip. There is a 20% chance of drawing a blue chip. The probability of drawing black is 0.3. The chance of drawing a red chip is 15%. A brown chip is as likely to be drawn as a red chip.Choosing a Car Color 7 out of 70 people chose white. 25% of the people chose black. 0.15 of the people chose red. 14 2 of the people chose blue. 1 6of the people chose brown. Choosing a Notebook Color 3 out of 20 people favored brown. 20% of the people favored blue. 1 4of the people favored black. 0.3 of the people favored red. Half as many people favored white as favored blue.Choosing a Sock Color 1 out of 8 socks sold are red. 25 5 of the socks sold are blue. 37 1 2% of the socks sold are black. 0.2 of the socks sold are white. Half as many brown socks are sold as white socks.

LESSON 26 Name Date Time Making Spinners continued 52 Copyright © Wright Group/McGraw-Hill

53 Copyright © Wright Group/McGraw-Hill STUDY LINK 27 Magnitude Estimates Name Date Time A magnitude estimateis a very rough estimate. It tells whether the exact answer falls in the tenths, ones, tens, hundreds, thousands, and so on. For each problem, make a magnitude estimate. Ask yourself: Is the answer in the tenths, ones, tens, hundreds, thousands, or ten-thousands? Circle the appropriate box. Do not solve the problems. Example:18 º 21 How I estimated 2. 12 º 708 How I estimated 4. 17 º 2.2 How I estimated 1. 73 º 28 How I estimated 3. 98 º 105 How I estimated 5. 2.6 º 3.9 How I estimated 0.1s 1s 10s 100s 10s100s 1,000s 10,000s 10s100s 1,000s 10,000s 10s 100s 1,000s 10,000s 10s100s 1,000s 10,000s 20 º20 400 10s100s 1,000s 10,000s Try This 6. Use the digits 4, 5, 6, and 8. Make as many factor pairs as you can that have a product between 3,000 and 5,000. Use a calculator to solve the problems. 250

LESSON 27 Name Date Time Extended Facts Copyright © Wright Group/McGraw-Hill 54 Directions  Shuffle the deck and draw two cards.  Record and multiply the numbers shown on the cards.  Then use your solution to write extended facts. Example: 1. ____________ º _____________ ____________ ____________ º 10 ____________ ____________ º 100 ____________ ____________ º 1000 ____________ 2. ____________ º _____________ ____________ ____________ º 10 ____________ ____________ º 100 ____________ ____________ º 1000 ____________ 3. ____________ º _____________ ____________ ____________ º 10 ____________ ____________ º 100 ____________ ____________ º 1000 ____________ 4. Explain how you use multiplication facts to help you solve problems with larger numbers. 5 5 7 7 5 ? 7 35 35 º 10 350 35 º 100 3,500 35 º 1,000 35,000

55 Copyright © Wright Group/McGraw-Hill STUDY LINK 28 Name Date Time  For each problem, make a magnitude estimate.  Circle the appropriate box. Do not solve the problem.  Then choose 3 problems to solve. Show your work on the grid. 1. 8 º 19 How I estimated 2. 155 º 6 How I estimated 3. 37 º 58 How I estimated 4. 5 º 4.2 How I estimated 5. 9.3 º 2.8 How I estimated 10s 100s 1,000s 10,000s 10s100s 1,000s 10,000s 10s 100s 1,000s 10,000s 10s 100s 1,000s 10,000s 10s 100s 1,000s 10,000s Estimating and Multiplying 247

LESSON 28 Name Date Time Copyright © Wright Group/McGraw-Hill 56 Materials  array grid (Math Masters,pp. 416 and 417)  base-10 blocks Directions  Draw a line around rows and columns on the grid to model each problem.  Cover the array you made using as few base-10 blocks as possible.  Solve using the partial-products method.  Then match each part of the array with a partial product.  Record the solution, filling in the sentences to match the blocks you used. 1. 6 º 23  In each of 6 rows there are…longs, so there are cubes. cubes, so there are cubes. There are cubes in all. Write the problem showing the partial products. In each of 20 rows there are… In each of 6 rows there are…longs, so there are cubes. cubes, so there are cubes. longs, so there are cubes. cubes, so there are cubes. There are cubes in all. Write the problem showing the partial products. 2. 26 º 18  Model the Partial-Products Method

57 Copyright © Wright Group/McGraw-Hill LESSON 28 Name Date Time A Mental Calculation Strategy When you multiply a number that ends in 9, you can simplify the calculation by changing it into an easier problem. Then adjust the result. Example 1:2 º 99 ?  Change 2 º 99 into 2 º 100.  Find the answer: 2 º 100 200  Ask: How is the answer to 2 º 100 different from the answer to 2 º 99? 100 is 1 more than 99, and you multiplied by 2. So 200 is 2 more than the answer to 2 º 99.  Adjust the answer to 2 º 100 to find the answer to 2 º 99: 200 2 198. So 2 º 99 198. Example 2:3 º 149 ?  Change 3 º 149 into 3 º 150.  Find the answer: 3 º 150 (3 º 100) (3 º 50) 450.  Ask: How is the answer to 3 º 150 different from the answer to 3 º 149? 150 is 1 more than 149, and you multiplied by 3. So 450 is 3 more than the answer to 3 º 149.  Adjust: 450 3 447. So 3 º 149 447. Use this strategy to calculate these products mentally. 1. 5 º 49 2. 5 º 99 3. 8 º 99 4. 4 º 199 5. 2 º 119 6. 3 º 98

LESSON 29 Name Date Time Lattice Multiplication Table 58 Copyright © Wright Group/McGraw-Hill 9 876543210 0 1 2 3 4 5 6 7 8 9 000000000 0 0 1 2 3 4 5 6 765443210 7 8 654321005443221 0 44332110 433221103222 1100 22 11 10000 0 0 0 0 0 11110000 0000000000000 00 0000 0 9 8 7 6 5 4 3 2 468 02468 2 1 34 567890 692 58147 826 04826 050 50505 284 06284 418 529630 0 0 0 0 0 642 086420876 543210

59 Copyright © Wright Group/McGraw-Hill STUDY LINK 29 Multiply with the Lattice Method Name Date Time For each problem:  Make a magnitude estimate. Circle the appropriate box.  Solve using the lattice method. Show your work in the grids. 1. 94 º 73  3. 5.4 º 6.18  5. 17.7 º 19.3  2. 24 º 3.7  4. 384 º 261  100s1,000s 10,000s 100,000s 0.1s 1s 10s 100s 0.1s 1s 10s 100s 0.1s 1s 10s 100s 10s100s 1,000s 10,000s 6. 7,402 2,587  7. 37 7 ∑ 8. 328 237  9. $15.75 $3.25  Practice 20

LESSON 29 Name Date Time An Ancient Multiplication Method Copyright © Wright Group/McGraw-Hill 60 Over 4,000 years ago, the Egyptians developed one of the earliest multiplication methods. This method, with some modifications, was then used by the ancient Greeks, and in the Middle Ages, by people living in other parts of Europe. Study the examples of the Egyptian method below. Each problem has been solved by this method of multiplication. Try to figure out how the method works. 13 º 25 18 º 17 26 º 31  806 306 325 ✓ ✓ ✓✓ ✓ ✓ ✓ ✓ 125(1 º 25) 250(2 º 25) 4 100(4 º 25) 8 200(8 º 25) 325 (13 º 25) 117 234 468 8 136 16 272 306 131 262 4 124 8 248 16 496 806 Make up a multiplication problem. Solve it using the Egyptian method. Then explain how the method works, using your problem as an example.

61 Copyright © Wright Group/McGraw-Hill STUDY LINK 210 Place-Value Puzzles 28 Name Date Time Use the clues to solve the puzzles. Puzzle 1 The value of the digit in thethousandthsplace is equal to the sum of the measures of the angles in a triangle (180°) divided by 30. If you multiply the digit in the tensplace by 1,000; the answer will be 9,000. Double 35. Divide the result by 10. Write the answer in the tenthsplace. The hundreds-place digit is 1 2the value of the digit in the thousandths place. When you multiply the digit in the onesplace by itself, the answer is 0. Write a digit in the hundredthsplace so that the sum of all six digits in this number is 30. What is the number?. Puzzle 2 Double 12. Divide the result by 8. Write the answer in the thousandsplace. If you multiply the digit in the hundredthsplace by 10, your answer will be 40. The tens-place digit is a prime number. If you multiply it by itself, the answer is 49. Multiply 7 and 3. Subtract 12. Write the answer in the thousandthsplace. Multiply the digit in the hundredths place by the digit in the thousands place. Subtract 7 from the result. Write the digit in the tenthsplace. The digit in the onesplace is an odd digit that has not been used yet. The value of the digit in the hundredsplace is the same as the number of sides of a quadrilateral. What is the number? ,. Check:The sum of the answers to both puzzles is 3,862.305. Millions Thousands Ones Hundred- Ten- Millions Hundred- Ten- Thousands Hundreds Tens Ones millions millions thousands thousands 3. 7,772 1,568  4. 472 228  5. 826 º 54  6. 59 / 3 ∑ Practice

LESSON 210 Name Date Time Number Stories and Estimation Copyright © Wright Group/McGraw-Hill 62 Read each number story carefully. Write an open number sentence to use in estimating. Answer the question. Example: It is said that the Aztec king, Montezuma, drank about 50 cups of chocolate per day. Did he drink moreor lessthan 10 gallons of chocolate in a week? (Hint: 16 cups 1 gallon) Open number sentence: Answer: 1. Certain varieties of seahorses can move 10.5 inches per minute. At this rate, could these seahorses be able to travel 6 yards in 1 hour? a. Open number sentence: b. Answer: 2. Orville Wright completed the first airplane flight on December 17, 1903. He traveled 120 feet in 12 seconds. If he had been able to stay in the air for a full minute, would he have traveled 1 mile? (Hint: 1 mile 5,280 feet) a. Open number sentence: b. Answer: 3. In 1960, the Triton became the first submarine to circumnavigate the world. It covered 36,014 miles in 76 days. Is that more or less than 100 miles per day? a. Open number sentence: b. Answer: Source: The Kids’ World Almanac of Records and Facts 10 º16 Number of cups in 10 gallon s more

63 Copyright © Wright Group/McGraw-Hill STUDY LINK 211 Unit 3: Family Letter Name Date Time Geometry Explorations and the American Tour In Unit 3, your child will set out on the American Tour, a yearlong series of mathematical activities examining historical, demographic, and environmental features of the United States. The American Tour activities will develop your child’s ability to read, interpret, critically examine, and use mathematical information presented in text, tables, and graphics. These math skills are vital in our technological age. Many American Tour activities rely on materials in the American Tour section of the Student Reference Book.This section—part historical atlas and part almanac—contains maps, data, and other information from a wide range of sources: the U.S. Census Bureau, the National Weather Service, and the National Geographic Society. Unit 3 also will review some geometry concepts from earlier grades while introducing and expanding on others. In Fourth Grade Everyday Mathematics,students used a compass to construct basic shapes and create geometric designs. In this unit, your child will extend these skills and explore concepts of congruent figures (same size, same shape), using a compass and straightedge. In addition, students will use another tool, the Geometry Template. It contains protractors and rulers for measuring, as well as cutouts for drawing a variety of geometric figures. Finally, students will explore the mathematics and art of tessellations—patterns of shapes that cover a surface without gaps or overlaps. They will use math tools to create their own designs. You can help your child by asking questions about information presented in newspaper and magazine tables and graphics. Also, the world is filled with many 2-dimensional and 3-dimensional geometric forms: angles, line segments, curves, cubes, cylinders, spheres, pyramids, and so on. Many wonderful geometric patterns can be seen in nature as well as in the things that people create. It will be helpful for you and your child to look for and talk about geometric shapes throughout the year. Please keep this Family Letter for reference as your child works through Unit 3.

acute angle An angle with a measure greater than 0 degrees and less than 90 degrees. adjacent angles Two angles with a common side and vertex that do not otherwise overlap. In the diagram, angles 1 and 2 are adjacent angles. Angles 2 and 3, angles 3 and 4, and angles 4 and 1 are also adjacent. congruent Having exactly the same shape and size. diameter A line segment that passes through the center of a circle (or sphere) and has endpoints on the circle (or sphere); also, the length of this line segment. The diameter of a circle or sphere is twice the length of its radius. equilateral triangle A triangle with all three sides the same length. In an equilateral triangle, all three angles have the same measure. obtuse angle An angle with a measure greater than 90 degrees and less than 180 degrees. radius A line segment from the center of a circle (or sphere) to any point on the circle (or sphere); also, the length of this line segment. right angle An angle with a measure of 90 degrees. tessellation An arrangement of shapes that covers a surface completely without overlaps or gaps. Also calledtiling. vertical (opposite) angles The angles made by intersecting lines that do not share a common side. Vertical angles have equal measures. In the diagram, angles 2 and 4 are a pair of vertical angles. Angles 1 and 3 are another pair of vertical angles. Vertical angles 1 3 42 A tessellation Right angle center radius Obtuse angle Equilateral triangles diameter diameter Congruent triangles Adjacent angles 1 3 42 Acute angle Vocabulary Important terms in Unit 3: Copyright © Wright Group/McGraw-Hill 64 Unit 3: Family Letter cont. STUDY LINK 211

Copyright © Wright Group/McGraw-Hill Do-Anytime Activities To work with your child on the concepts taught in this unit and in previous units, try these interesting and rewarding activities: 1. Together, read the book A Cloak for the Dreamerby Marilyn Burns. 2. When you are at home or at a store, ask your child to identify different types of polygons such as triangles, squares, pentagons, and hexagons. 3. Visit the Web site for the U.S. Bureau of the Census at http://www.census.gov/. Have your child write three interesting pieces of information that he or she learned from the Web site. 4. Look for examples of bar graphs in newspapers or magazines. Ask your child to explain the information shown by a graph. In Unit 3, your child will practice geometry and computation skills by playing the following games. For detailed instructions, see the Student Reference Book. Angle TangleSeeStudent Reference Book,page 296 Two players will need a protractor and a straightedge to play this game. Playing Angle Tanglegives students practice in drawing and measuring angles. High-Number Toss: Decimal VersionSeeStudent Reference Book,page 321 This game practices concepts of place value and standard notation. It requires 2 players and number cards 0–9 (4 of each). Multiplication Top-ItSeeStudent Reference Book,page 334 This game practices the basic multiplication facts. It requires a deck of cards with 4 each of the numbers 1–10, and can be played by 2– 4 players. Polygon CaptureSeeStudent Reference Book,page 328 This game uses 16 polygons and 16 Property Cards, and is played by partners or 2 teams each with 2 players. Polygon Capturepractices identifying properties of polygons related to sides and angles. Building Skills through Games Unit 3: Family Letter cont. STUDY LINK 211 65

Study Link 3 1 1.Illinois 2.851,000; 4,822,000; 8,712,000; 12,051,000 3. 3,971,000 4. 3,890,000 5. 3,339,000 6.The population increases by about 4,000,000 every fifty years. 7. About 16,000,000 8. About 14,000,000 Study Link 3 2 1. A 2. 5,472,000 3. H 4. a. About 250,000,000 b. About 55% Study Link 3 3 1. 60°; 90°; 60° 2. 120°; 60°; 60° 3. 90°; 135°; 135° 4. 30°; 75° Study Link 3 4 1. 70° 2. 50° 3. 110° 4. 130° 5. 60° 6. 180° 7. 120° 8. 90° 9. 50° 10. 150° 11. 170° Study Link 3 5 1. acute; 12° 2. acute; 65° 3. obtuse; 103° 4. Sample answer: Angle Dand angle E 5. Sample answer: Angle Dand angle F 6. Sample answer: Angle Gand angle H 9. 14,670 11. 11R1 Study Link 3 6 1. scalene 2. isosceles 3. isosceles; right 4. equilateral; isosceles 5. Objects and types of angles vary. 6. 11,761 7. 5,750 8. 42,405 9. 11 Study Link 3 7 Sample answers are given for Problems 1–5. 1. The pentagon is the only shape that is not regular. 2. The oval is the only shape that is curved. 3. The crossed-out shape is the only shape that is not convex. 4. The trapezoid is the only shape without two pairs of parallel sides. Study Link 3 8 1.–3. Samples of tessellations vary. Study Link 3 9 1. Sample answer: Draw a line between two of the vertices to create two triangles. Since the sum of the angles in each triangle is 180°, the sum of the angles in a quadrangle is 360°. 2. 360° 3. a.–b. c.–d. Study Link 3 10 1. Sample answers are given. a. b. c. d. 2. 3. a. 2 b. 70° c. 360° d. trapezoid 90° 50° 130° 130° 50° 40° D B C A tear tear teartear DC B A Copyright © Wright Group/McGraw-Hill Unit 3: Family Letter cont. STUDY LINK 211 66 As You Help Your Child with Homework As your child brings assignments home, you may want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through this unit’s Study Links.